2 research outputs found
On the characterization of models of H*: The semantical aspect
We give a characterization, with respect to a large class of models of
untyped lambda-calculus, of those models that are fully abstract for
head-normalization, i.e., whose equational theory is H* (observations for head
normalization). An extensional K-model is fully abstract if and only if it
is hyperimmune, {\em i.e.}, not well founded chains of elements of D cannot be
captured by any recursive function.
This article, together with its companion paper, form the long version of
[Bre14]. It is a standalone paper that presents a purely semantical proof of
the result as opposed to its companion paper that presents an independent and
purely syntactical proof of the same result
Relational Graph Models at Work
We study the relational graph models that constitute a natural subclass of
relational models of lambda-calculus. We prove that among the lambda-theories
induced by such models there exists a minimal one, and that the corresponding
relational graph model is very natural and easy to construct. We then study
relational graph models that are fully abstract, in the sense that they capture
some observational equivalence between lambda-terms. We focus on the two main
observational equivalences in the lambda-calculus, the theory H+ generated by
taking as observables the beta-normal forms, and H* generated by considering as
observables the head normal forms. On the one hand we introduce a notion of
lambda-K\"onig model and prove that a relational graph model is fully abstract
for H+ if and only if it is extensional and lambda-K\"onig. On the other hand
we show that the dual notion of hyperimmune model, together with
extensionality, captures the full abstraction for H*